document.write( "Question 1062034: Let A: $\"R%5E3+-%3ER%5E2\"$ and B: $\"R%5E2+-%3ER%5E3\"$ , so that BA: $\"R%5E3+-%3ER%5E3\"$ . Is BA an invertible map? \n" ); document.write( "

Algebra.Com's Answer #676794 by ikleyn(52784) $\"\"$ $\"About$

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\n" ); document.write( "1. Not necessary. \r
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\n" ); document.write( "\n" ); document.write( "2. Not if A and B are linear operators.\r
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\n" ); document.write( "\n" ); document.write( "3. Not as a rule.\r
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\n" ); document.write( "\n" ); document.write( "4. But since $\"R%5E3\"$ and $\"R%5E2\"$ have the same cardinality, there are (do exist) some maps A and B (highly non-linear) that BA can be invertible.\r
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